NEW YORK - In their highest-profile gig to date, Philadelphia new-music stars the Crossing brought their biggest-ever project to Lincoln Center and scored a triumph. Whoops and cheers greeted director Donald Nally, his singers, and their instrumentalist colleagues after both of their concerts Sunday at the Mostly Mozart Festival.

The audience's response was all the more striking because, on paper, the program wouldn't seem a crowd-pleaser: 31/2 hours in which seven composers (only one remotely a marquee name) offer their riffs on a downbeat 17th-century contemplation of a dying man's body parts.

That dying man was Jesus Christ on the cross; the contemplation was Membra Jesu Nostri, a cycle of seven cantatas, one per body part, by Dietrich Buxtehude, the musician Bach walked 200 miles to hear. The project was "Seven Responses" (one composer responding to each body-part cantata), conceived by Nally for the Crossing with the period-instrument group Quicksilver and the International Contemporary Ensemble. It premiered in late June at the Philadelphia Episcopal Cathedral.

The question mark over the New York performance was about the change of venue: How would music that seemed so effective in a warm, dark church come across in the matter-of-fact plainness of Merkin Concert Hall, one of Manhattan's less-charactered venues?

The answer: astonishingly well. Whatever was lost in atmosphere was more than made up for in immediacy; the presence of the sound was palpable, and the closer view of the performers made a slew of details clearer.

As a result, my mind was completely changed about some of the pieces. In June, Caroline Shaw's "To the Hands" had seemed to me a tendentious, poorly explained plea for global refugees, with bleeding chunks of Buxtehude thrown in. On Sunday, I could appreciate both the skill with which Shaw (re)worked the earlier music into her score, and her sincere approach to the subject.

The first time around, Anna Thorvaldsdottir's "Ad genua/To the Knees" and Santa Ratniece's "My soul will sink within me" struck my ears as ethereal loveliness, with some funky harmonies and different timbres included for effect. In the smaller space, I was moved by the austere beauty of Maren Brehm's alto solo in the Thorvaldsdottir and thrilled by how Ratniece slipped woozy, off-kilter harmonies and marvelously weird sound effects in and out of the choir's luminous chords.

Most striking was the percussionist's monologue in Pelle Gudmundsen-Holmgreen's "Ad cor/To the Heart," which in the cathedral came across as merely cynical, and at close range turned out to be a piece of deadpan wit. The difference was that we could see the funny noises Ross Karre made with his instruments as he spoke his lines.

After the second concert, a friend told me it was a privilege to be in a room with so many gifted people performing music that was so interesting and so unusual. He was right: We were privileged to be there Sunday, Philadelphia was fortunate to be the birthplace of this project, and New York is lucky that we're willing to share the Crossing with it.